'Journey to the Center of a Triangle' (1976) 8m, dir. Bruce & Katharine Cornwell. Another fabulous film by the Cornwells, created on the Tektronics 4051 Graphics Terminal. Presents a series of animated constructions that determine the center of a variety of triangles, including such centers as circumcenter, incenter, centroid and orthocenter. The music is Bach's preludes 8 (Eb minor) and 12 (F minor) from the Well Tempered Clavier. More on the Cornwells at http://www.afana.org/cornwell.htm
According to son Eric Cornwell, here's how the film was made: The 4051 produced only black and green vector images, not even grey scale. The film's scenes were divided into layers in the programming, one layer for each of the colors in the scene, and each was shot separately onto high-contrast fine-grained b&w film stock. The final scene in "Journey" had 5 layers: one for each of the four colored dots, plus one for the white triangle and line.
These five clips were then multiple-exposed onto color film on an optical printer, using colored filters to add the desired color to each black&white layer as it was copied. The resulting color was much better than a film of an RGB display would have been because the color filters on the optical printer allowed access to the full range of the color negative film, allowing much more saturated colors. All of that color is pretty much lost now, between prints fading and/or transfers to the VHS, and then viewing them on a computer screen which has a much more limited color gamut. Please imagine it all in bright, brilliant colors.
June 27, 2019 Subject:
beautiful and insightful animations
This program shows excellent geometric animations. Watching these animations is almost like attending a good math lecture.
January 30, 2017 Subject:
solo puedo decir , lo maravilloso que es e arte de unir con maestría absoluta , la música y la geometría ,, fantástico , los felicito, esta experiencia de ver , es mi primera vez que entro a este sitio web,, son todos los que componen este monumental sitio ,, gente de un inmenso espíritu dadivoso , y altruista ,, héctor luis... titolio21... soy chileno 62 años.. espero seguir disfrutando de este gran sitio.. si alguien vée este comentario,, me gustaría mucho que alguien me ayudara a encontrar antecedentes referente a los incendios forestales,, estamos sufriendo a peor catástrofe de la historia de mi país,,necesitamos mucha ayuda,, cordiamente un chileno de corazón..
August 31, 2014 Subject:
July 12, 2014 Subject:
One of many amazing works by the Cornwell's, and thanks to AFANA and the sponsor for making it readily accessible. Though few of their works are extant (Congruent Triangles is also here at the Archive), I've seen approx. 20 other titles, all revealing a Zen-like minimalism generating genuine lyricism. Math was not my strong suit as a younger man, but I never had a teacher like the Cornwell's.
This is epic in its own simple/complex way, and the bio and filmog of the Cornwell's at AFANA is a long-past-due capsule portrait of this pair of quietly titanic artists.
July 1, 2013 Subject:
This is a good video.
May 6, 2011 Subject:
Plane geometry has never looked this cool!
A truly amazing "lecture" on the four classical centers of a triangle. Done entirely without any narration or explanation, repeated examples show how to construct, apparently with a compass and straightedge, the centers set to a downright somnolent piece of music.
The final, "The Grand Tour", is a more amazing (if that's possible) animation showing the movement of these points as a triangle evolves set to a snappy classical tune.
Definitely worth watching. If you get bored, just fast forward to 7:15
December 27, 2010 Subject:
Minimal and beautiful
Minimal and beautiful animation, including a gentle soundtrack. Worth watching for sure, the end section is very cool.